Accessing Geometric Elements

The main communication between CindyScript and the geometry part of Cinderella is accomplished by accessing the geometric objects of a construction.
Geometric elements can be accessed in two different ways: either one can access an element by the name of its label or one can access lists of elements by special CindyScript operators.
The interaction between Cinderella and CindyScript gives CindyScript the possibility to read essentially all properties of the elements of a geometric construction.
Most properties can also be set by CindyScript.
The following sections first describe the possible ways to address geometric objects and then provide a detailed list of the supported properties.

Accessing Elements by Their Names

Every element in a geometric construction has a unique name, its label.
This name can be used as a handle in CindyScript.
Formally, in CindyScript the element plays the role of a predefined variable.
The different properties can be read and set via the . operator (dot operator).
For instance, the line of code

A.size=20

sets the size of point A in a construction to the value 20.
If a point or a line is contained in an arithmetic operator without a dot operator, then it is automatically converted to a vector representing its position.
Thus a point is converted into an [x,y] vector representing its two-dimensional coordinates.
A line is converted to an [x,y,z] vector representing its homogeneous coordinates.
However,if one intends to set the coordinates of a point, then one has to use the dot operator explicitly.
If a handle to a geometric object is not used in an arithmetic expression, then it is still passed to the calculation as the geometric object.
Since these concepts are a bit subtle, we will clarify them with a few examples.

Assume that A, B, and C are points in a Cinderella construction.
The line

A.xy=(B+C)/2

sets the point A to be the midpoint of B and C.
These two points are contained in an arithmetic expression, and therefore they are immediately inverted to an [x,y] vector.
Setting the position of point A has to be done by explicitly using the .xy property.

The following program sets the color of all three points to green:

pts=[A,B,C];
forall(pts,p,
p.color=[0,1,0];
)

In this code the point names are passed as handles to the list pts.
Traversing the list with the forall operator puts this handles one after the other into the variable p, from which their color property is accessed.

Lists of Elements

Sometimes it is not necessary to access points individually by their name.
In particular, this happens whenever one is interested in performing an operation on all points in a construction.
This may happen, for instance, when one wants to calculate the convex hull of a point set.
For this, CindyScript provides several operators that return lists of elements.
For instance, the operator allpoints() returns a list of all points of a construction.
We will demonstrate this with a very tiny example.
The following program changes the color of the points depending on their position relative to the y-axis:

The following picture shows the application of the code to a random collection of points.

Properties of Geometric Objects

We now start with a complete description of all properties that are currently accessible via CindyScript.
Every property is at least readable.
For each property we list the type of value expected for the property, whether it is read only or also writeable, and a short description of its purpose.
Possible property types are usually as follows:

real:
a real number

int:
an integer number

bool:
either true or false

string:
a sequence of characters

2-vector:
a two-dimensional vector

3-vector:
a three-dimensional vector

3x3-matrix:
a 3 by 3 matrix

Some properties, like the current position, are only writable for free objects.
We mark this by the word “free” in the corresponding column.

Properties Common to All Geometric Objects

Name

Writeable

Type

Purpose

color

yes

3-vector

The (red, green, blue) color vector of the object

colorhsb

yes

3-vector

The (hue, saturation, black) color vector of the object

isshowing

yes

bool

Whether the object is shown (this is inherited by all elements that depend on the object)

visible

yes

bool

Whether the object is shown (not inherited by dependent objects)

alpha

yes

real

The opacity of the object (between 0.0 and 1.0)

labeled

yes

bool

Whether the object shows its label

name

no

string

The label of the object

caption

yes

string

A caption that may replace the name

trace

yes

bool

Whether the object leaves a trace

tracelength

yes

int

The length of the trace

selected

yes

bool

Whether the object is currently selected

Each geometric element has a unique name.
the string that represents this name may be accessed by .name.
So for instance A.name returns the string "A".
The name may not be identical with the caption of the element shown in the construction.
If A.caption is the empty string the name is shown, otherwise the caption.

Properties of Points

Name

Writeable

Type

Purpose

x

free

real

The x-coordinate of the point

y

free

real

The y-coordinate of the point

xy

free

2-vector

The xy-coordinates of the point

coord

free

2-vector

The xy-coordinates of the point

homog

free

3-vector

The homogeneous coordinates of the point

angle

free

real

Applies only to PointOnCircle objects. The angle of the point on the circle

size

yes

int

The size of the point (0..40)

imagerot

yes

real

A rotation angle if the point is equipped with an image

Properties of Lines

Name

Writeable

Type

Purpose

homog

free

3-vector

The homogeneous coordinates of the line

angle

free

real

The angle of the line

slope

free

real

The slope of the line

size

yes

int

The size of the line (0..10)

Properties of Circles and Conics

Name

Writeable

Type

Purpose

center

no

real

The center of the circle

radius

free

real

The radius of the circle

matrix

no

real

The matrix describing the quadratic form of the circle or conic

dualMatrix

no

real

The matrix describing the dual (=adjoint) matrix of the conic

size

yes

int

The size of the border line (0..10)

Properties of Texts

Name

Writeable

Type

Purpose

text

yes

string

The content of the text

pressed

yes

boolean

The state of this text if it is a button

xy

yes

2-vector

The position of the text

Properties of Animations

Name

Writeable

Type

Purpose

run

yes

bool

Whether the animation is running

speed

yes

real

The relative animation speed

Properties of Transformations

Name

Writeable

Type

Purpose

matrix

no

3x3 matrix

The homogeneous matrix of the transformation

inverse

no

3x3 matrix

The homogeneous matrix of the inverse transformation

Properties of CindyLab Objects

It is not only geometric properties that can be accessed by CindyScript.
The simulation parameters of CindyLab constructions can also be read and sometimes set via CindyScript.

Properties of All CindyLab Elements

Name

Writeable

Type

Purpose

simulate

yes

bool

Whether the object takes part in the physics simulation or is neglected

Properties of Masses

Name

Writeable

Type

Purpose

mass

yes

real

The mass of the object

charge

yes

int

The charge of the object

friction

yes

real

The individual friction of the object

radius

yes

real

The radius if the mass is treated as a ball

posx

yes

real

The x-component of the mass's position

posy

yes

real

The y-component of the mass's position

pos

yes

2-vector

The mass's position vector

vx

yes

real

The x-component of the velocity

vy

yes

real

The y-component of the velocity

v

yes

2-vector

The velocity vector

fx

no

real

The x-component of the force acting on the particle

fy

no

real

The y-component of the force acting on the particle

f

no

2-vector

The force vector acting on the particle

kinetic

no

real

The kinetic energy of the particle

ke

no

real

The kinetic energy of the particle

Sometimes one is interested to add a user defined force potential between masses.
This can be done by scripting a suitable piece of code in the Integeration Tick event.
Since internally the position of masses has a finer time scale than usual geometric movements it is necessary to access their position via the pos, posx and posy accessors.

Properties of Springs and Coulomb Forces

Name

Writeable

Type

Purpose

l

no

real

The current length of the spring

lrest

no

real

The rest length of the spring

ldiff

no

real

The distance to the rest length of the spring

strength

yes

real

The spring constant

f

no

real

The force vector caused by the spring

amplitude

yes

real

The amplitude for actuation

speed

yes

real

The speed for actuation

phase

yes

real

The phase for actuation (between 0.0 and 1.0)

potential

no

real

The potential energy in the spring

pe

no

real

The potential energy in the spring

Property for Velocities

Name

Writeable

Type

Purpose

factor

yes

real

The multiplication factor between graphical representation and actual velocity

Properties of Gravity

Name

Writeable

Type

Purpose

strength

yes

real

The strength of the gravity field

potential

no

real

The potential energy of all masses in the gravity field

pe

no

real

The potential energy of all masses in the gravity field

Properties of Suns

Name

Writeable

Type

Purpose

mass

yes

real

The mass of the sun

potential

no

real

The potential energy of all masses in the sun field

pe

no

real

The potential energy of all masses in the sun field

Properties of Magnetic Areas

Name

Writeable

Type

Purpose

strength

yes

real

The strength of the magnetic field

friction

yes

real

The friction in the magnetic area

Properties of Bouncers and Floors

Name

Writeable

Type

Purpose

xdamp

yes

real

Damping in the x-direction

ydamp

yes

real

Damping in the y-direction

Properties of the Environment

The environment can be accessed by the built-in operator simulation().
The following slots of the environment can be accessed:

Name

Writeable

Type

Purpose

gravity

yes

real

The global gravity

friction

yes

real

The global friction

kinetic

no

real

The overall kinetic energy

ke

no

real

The overall kinetic energy

potential

no

real

The overall potential energy

pe

no

real

The overall potential energy

Inspecting Elements

You can also use the generic CindyScript function inspect(‹element›) to access all the attributes that are available in the Inspector.
For example, if a point A exists in the construction, the function

Using the two-parameter form inspect(‹element›,‹string›) you can read all the attributes of A that are listed in the above array:

inspect(A,"text.fontfamily")

returns

SansSerif

With the three-parameter form inspect(‹element›,‹string›,‹expr›) you can also set the attributes that are not read-only (for example, you cannot change the list of incidences or the definition of an element).
The following function will set the font of A to a Serif font:

inspect(A,"text.fontfamily","Serif")

The inspect command is very powerful, as you can automate all actions you normally would have to do in the Inspector using the mouse.
Also, it gives you fine grained control over all properties.

Set a user attribute: attribute(‹geo›,‹string1›,‹string2›)

Not available in CindyJS yet!

Description:
Sets the user attribute of ‹geo› identified by ‹string1› to the value ‹string2›.

Read a user attribute: attribute(‹geo›,‹string›)

Both versions of the attribute function are mainly used for interaction with the Visage Extension of Cinderella, which has not been ported to CindyJS yet.

Creating and Destroying Elements

Starting with Cinderella version 2.1 you can also create points on the fly from CindyScript.
The function

p = createpoint("A",[4,6])

creates a point labeled A at coordinates [4,6], unless there is already an element A.
If it exists, it will be moved to the position given as second argument.
The value of the function is the point or the already existing element A.
This means that repeated executions of the function are not harmful to your code - if you need a free point at “A” you can ensure that it exists using the createpoint-command.

Using the removeelement function you can also remove elements from your construction.
Be aware that all dependent elements will be removed as well.
The function expects an element as argument, so you can use either